Very few. Access in the Dales is club based, so either there is free access or "ask at the farm", and insurance status is not asked about, or if there is a permit system, permits are available to clubs only and not individual cavers, irrespective of DIM status.
The sites I mention above where we're working on organising access are actually on a personal basis (not club based) and having the ability to show a card (to demonstrate cover) has certainly helped smooth things over.
